IMO 2021, Problem 6
Posted: Wed Jul 21, 2021 8:21 pm
Let $m \ge 2$ be an integer, $A$ be a finite set of (not necessarily positive) integers, and $B_1,B_2, B_3, \ldots, B_m$ subsets of $A$. Assume that for each $k=1,2,...,m$, the sum of the elements of $B_k$ is $m^k$. Prove that $A$ contains at least $m/2$ elements.